Reconstruction by weighted correlation for MRI with time-varying gradients

Motion and temporal B0-shift corrections for QSM and R 2 * mapping using dual-echo spiral navigators and conjugate-phase reconstruction

PURPOSE

To develop an efficient navigator-based motion and temporal B0-shift correction technique for 3D multi-echo gradient-echo (ME-GRE) MRI for quantitative susceptibility mapping (QSM) andR 2 * $$ {\mathrm{R}}_2^{\ast } $$ mapping.

THEORY AND METHODS

A dual-echo 3D stack-of-spiral navigator was designed to interleave with the Cartesian multi-echo gradient-echo acquisitions, allowing the acquisition of both low-echo and high-echo time signals. We additionally designed a novel conjugate phase-based reconstruction method for the joint correction of motion and temporal B0 shifts. We performed numerical simulation, phantom scans, and in vivo human scans to assess the performance of the methods.

RESULTS

Numerical simulation and human brain scans demonstrated that the proposed technique successfully corrected artifacts induced by both head motions and temporal B0 changes. Efficient B0-change correction with conjugate-phase reconstruction can be performed on fewer than 10 clustered k-space segments. In vivo scans showed that combining temporal B0 correction with motion correction further reduced artifacts and improved image quality in bothR 2 * $$ {\mathrm{R}}_2^{\ast } $$ and QSM images.

CONCLUSION

Our proposed approach of using 3D spiral navigators and a novel conjugate-phase reconstruction method can improve susceptibility-related measurements using MR.

Off-resonance artifact correction for MRI: A review

In magnetic resonance imaging (MRI), inhomogeneity in the main magnetic field used for imaging, referred to as off-resonance, can lead to image artifacts ranging from mild to severe depending on the application. Off-resonance artifacts, such as signal loss, geometric distortions, and blurring, can compromise the clinical and scientific utility of MR images. In this review, we describe sources of off-resonance in MRI, how off-resonance affects images, and strategies to prevent and correct for off-resonance. Given recent advances and the great potential of low-field and/or portable MRI, we also highlight the advantages and challenges of imaging at low field with respect to off-resonance.

Superconducting magnet designs and MRI accessibility: A review

Presently, magnetic resonance imaging (MRI) magnets must deliver excellent magnetic field (B₀ ) uniformity to achieve optimum image quality. Long magnets can satisfy the homogeneity requirements but require considerable superconducting material. These designs result in large, heavy, and costly systems that aggravate as field strength increases. Furthermore, the tight temperature tolerance of niobium titanium magnets adds instability to the system and requires operation at liquid helium temperature. These issues are crucial factors in the disparity of MR density and field strength use across the globe. Low-income settings show reduced access to MRI, especially to high field strengths. This article summarizes the proposed modifications to MRI superconducting magnet design and their impact on accessibility, including compact, reduced liquid helium, and specialty systems. Reducing the amount of superconductor inevitably entails shrinking the magnet size, resulting in higher field inhomogeneity. This work also reviews the state-of-the-art imaging and reconstruction methods to overcome this issue. Finally, we summarize the current and future challenges and opportunities in the design of accessible MRI.

Image distortion correction for MRI in low field permanent magnet systems with strong B0 inhomogeneity and gradient field nonlinearities

Objective

To correct for image distortions produced by standard Fourier reconstruction techniques on low field permanent magnet MRI systems with strong \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 inhomogeneity and gradient field nonlinearities.

Materials and methods

Conventional image distortion correction algorithms require accurate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta B}_{0}$$\end{document}ΔB0 maps which are not possible to acquire directly when the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 inhomogeneities also produce significant image distortions. Here we use a readout gradient time-shift in a TSE sequence to encode the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 field inhomogeneities in the k-space signals. Using a non-shifted and a shifted acquisition as input, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 maps and images were reconstructed in an iterative manner. In each iteration, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 maps were reconstructed from the phase difference using Tikhonov regularization, while images were reconstructed using either conjugate phase reconstruction (CPR) or model-based (MB) image reconstruction, taking the reconstructed field map into account. MB reconstructions were, furthermore, combined with compressed sensing (CS) to show the flexibility of this approach towards undersampling. These methods were compared to the standard fast Fourier transform (FFT) image reconstruction approach in simulations and measurements. Distortions due to gradient nonlinearities were corrected in CPR and MB using simulated gradient maps.

Results

Simulation results show that for moderate field inhomogeneities and gradient nonlinearities, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 maps and images reconstructed using iterative CPR result in comparable quality to that for iterative MB reconstructions. However, for stronger inhomogeneities, iterative MB reconstruction outperforms iterative CPR in terms of signal intensity correction. Combining MB with CS, similar image and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 map quality can be obtained without a scan time penalty. These findings were confirmed by experimental results.

Discussion

In case of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 inhomogeneities in the order of kHz, iterative MB reconstructions can help to improve both image quality and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 map estimation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10334-021-00907-2.

Deblurring for spiral real-time MRI using convolutional neural networks

PURPOSE

To develop and evaluate a fast and effective method for deblurring spiral real-time MRI (RT-MRI) using convolutional neural networks.

METHODS

We demonstrate a 3-layer residual convolutional neural networks to correct image domain off-resonance artifacts in speech production spiral RT-MRI without the knowledge of field maps. The architecture is motivated by the traditional deblurring approaches. Spatially varying off-resonance blur is synthetically generated by using discrete object approximation and field maps with data augmentation from a large database of 2D human speech production RT-MRI. The effect of off-resonance range, shift-invariance of blur, and readout durations on deblurring performance are investigated. The proposed method is validated using synthetic and real data with longer readouts, quantitatively using image quality metrics and qualitatively via visual inspection, and with a comparison to conventional deblurring methods.

RESULTS

Deblurring performance was found superior to a current autocalibrated method for in vivo data and only slightly worse than an ideal reconstruction with perfect knowledge of the field map for synthetic test data. Convolutional neural networks deblurring made it possible to visualize articulator boundaries with readouts up to 8 ms at 1.5 T, which is 3-fold longer than the current standard practice. The computation time was 12.3 ± 2.2 ms per frame, enabling low-latency processing for RT-MRI applications.

CONCLUSION

Convolutional neural networks deblurring is a practical, efficient, and field map-free approach for the deblurring of spiral RT-MRI. In the context of speech production imaging, this can enable 1.7-fold improvement in scan efficiency and the use of spiral readouts at higher field strengths such as 3 T.

Deconvolution-based distortion correction of EPI using analytic single-voxel point-spread functions

PURPOSE

To develop a postprocessing algorithm that corrects geometric distortions due to spatial variations of the static magnetic field amplitude, B₀ , and effects from relaxation during signal acquisition in EPI.

THEORY AND METHODS

An analytic, complex point-spread function is deduced for k-space trajectories of EPI variants and applied to corresponding acquisitions in a resolution phantom and in human volunteers at 3 T. With the analytic point-spread function and experimental maps of B₀ (and, optionally, the effective transverse relaxation time, T 2 * ) as input, a point-spread function matrix operator is devised for distortion correction by a Thikonov-regularized deconvolution in image space. The point-spread function operator provides additional information for an appropriate correction of the signal intensity distribution. A previous image combination algorithm for acquisitions with opposite phase blip polarities is adapted to the proposed method to recover destructively interfering signal contributions.

RESULTS

Applications of the proposed deconvolution-based distortion correction ("DecoDisCo") algorithm demonstrate excellent distortion corrections and superior performance regarding the recovery of an undistorted intensity distribution in comparison to a multifrequency reconstruction. Examples include full and partial Fourier standard EPI scans as well as double-shot center-out trajectories. Compared with other distortion-correction approaches, DecoDisCo permits additional deblurring to obtain sharper images in cases of significant T 2 * effects.

CONCLUSION

Robust distortion corrections in EPI acquisitions are feasible with high quality by regularized deconvolution with an analytic point-spread function. The general algorithm, which is publicly released on GitHub, can be straightforwardly adapted for specific EPI variants or other acquisition schemes.

Short-T2 MRI: Principles and recent advances

Among current modalities of biomedical and diagnostic imaging, MRI stands out by virtue of its versatile contrast obtained without ionizing radiation. However, in various cases, e.g., water protons in tissues such as bone, tendon, and lung, MRI performance is limited by the rapid decay of resonance signals associated with short transverse relaxation times T₂ or T₂*. Efforts to address this shortcoming have led to a variety of specialized short-T₂ techniques. Recent progress in this field expands the choice of methods and prompts fresh considerations with regard to instrumentation, data acquisition, and signal processing. In this review, the current status of short-T₂ MRI is surveyed. In an attempt to structure the growing range of techniques, the presentation highlights overarching concepts and basic methodological options. The most frequently used approaches are described in detail, including acquisition strategies, image reconstruction, hardware requirements, means of introducing contrast, sources of artifacts, limitations, and applications.

Calibration-Free B0 Correction of EPI Data Using Structured Low Rank Matrix Recovery

We introduce a structured low rank algorithm for the calibration-free compensation of field inhomogeneity artifacts in echo planar imaging (EPI) MRI data. We acquire the data using two EPI readouts that differ in echo-time. Using time segmentation, we reformulate the field inhomogeneity compensation problem as the recovery of an image time series from highly undersampled Fourier measurements. The temporal profile at each pixel is modeled as a single exponential, which is exploited to fill in the missing entries. We show that the exponential behavior at each pixel, along with the spatial smoothness of the exponential parameters, can be exploited to derive a 3-D annihilation relation in the Fourier domain. This relation translates to a low rank property on a structured multi-fold Toeplitz matrix, whose entries correspond to the measured k-space samples. We introduce a fast two-step algorithm for the completion of the Toeplitz matrix from the available samples. In the first step, we estimate the null space vectors of the Toeplitz matrix using only its fully sampled rows. The null space is then used to estimate the signal subspace, which facilitates the efficient recovery of the time series of images. We finally demonstrate the proposed approach on spherical MR phantom data and human data and show that the artifacts are significantly reduced.

Magnetic resonance fingerprinting with dictionary-based fat and water separation (DBFW MRF): A multi-component approach

Purpose

To obtain a fast and robust fat‐water separation with simultaneous estimation of water T₁, fat T₁, and fat fraction maps.

Methods

We modified an MR fingerprinting (MRF) framework to use a single dictionary combination of a water and fat dictionary. A variable TE acquisition pattern with maximum TE = 4.8 ms was used to increase the fat–water separability. Radiofrequency (RF) spoiling was used to reduce the size of the dictionary by reducing T₂ sensitivity. The technique was compared both in vitro and in vivo to an MRF method that incorporated 3‐point Dixon (DIXON MRF), as well as Cartesian IDEAL with different acquisition parameters.

Results

The proposed dictionary‐based fat–water separation technique (DBFW MRF) successfully provided fat fraction, water, and fat T₁, B₀, and B₁₊ maps both in vitro and in vivo. The fat fraction and water T₁ values obtained with DBFW MRF show excellent agreement with DIXON MRF as well as with the reference values obtained using a Cartesian IDEAL with a long TR (concordance correlation coefficient: 0.97/0.99 for fat fraction–water T₁). Whereas fat fraction values with Cartesian IDEAL were degraded in the presence of T₁ saturation, MRF methods successfully estimated and accounted for T₁ in the fat fraction estimates.

Conclusion

The DBFW MRF technique can successfully provide T₁ and fat fraction quantification in under 20 s per slice, intrinsically correcting T₁ biases typical of fast Dixon techniques. These features could improve the diagnostic quality and use of images in presence of fat.

Correcting image blur in spiral, retraced in/out (RIO) acquisitions using a maximized energy objective

PURPOSE

Images acquired with spiral k-space trajectories can suffer from off-resonance image blur. Previous work showed that averaging 2 images acquired with a retraced, in/out (RIO) trajectory self-corrects image blur so long as off-resonant spins accrue less than 1 half-cycle of relative phase over the readout. Practical scenarios frequently exceed this threshold. Here, we derive and characterize a more-robust off-resonance image blur correction method for RIO acquisitions.

METHODS

Phantom and human volunteer data were acquired using a RIO trajectory with readout durations ranging from 4 to 60 ms. The resulting images were deblurred using 3 candidate methods: conventional linear correction of the component images; semiautomatic deblurring of the component images using an established minimized phase objective function; and semiautomatic deblurring of the average of the component images using a maximized energy objective function, derived below. Deblurring errors were estimated relative to images acquired with 4 ms readouts.

RESULTS

All 3 methods converged to similar solutions in cases where less than 2 and 4 cycles of phase accrued over the readout in in vivo and phantom images, respectively (<13 ms readout at 3T). Above this threshold, the linear and minimized phase methods introduced several errors. The maximized energy function provided accurate deblurring so long as less than 6 and 10 cycles of phase accrued over the readout in in vivo and phantom images, respectively (<34 ms readout at 3T).

CONCLUSION

The maximized energy objective function can accurately deblur RIO acquisitions over a wide spectrum of off resonance frequencies.

Encoding and readout strategies in magnetic resonance elastography

Magnetic resonance elastography (MRE) has evolved significantly since its inception. Advances in motion-encoding gradient design and readout strategies have led to improved encoding and signal-to-noise ratio (SNR) efficiencies, which in turn allow for higher spatial resolution, increased coverage, and/or shorter scan times. The purpose of this review is to summarize MRE wave-encoding and readout approaches in a unified mathematical framework to allow for a comparative assessment of encoding and SNR efficiency of the various methods available. Besides standard full- and fractional-wave-encoding approaches, advanced techniques including flow compensation, sample interval modulation and multi-shot encoding are considered. Signal readout using fast k-space trajectories, reduced field of view, multi-slice, and undersampling techniques are summarized and put into perspective. The review is concluded with a foray into displacement and diffusion encoding as alternative and/or complementary techniques.

Rapid anatomical brain imaging using spiral acquisition and an expanded signal model

We report the deployment of spiral acquisition for high-resolution structural imaging at 7T. Long spiral readouts are rendered manageable by an expanded signal model including static off-resonance and B₀ dynamics along with k-space trajectories and coil sensitivity maps. Image reconstruction is accomplished by inversion of the signal model using an extension of the iterative non-Cartesian SENSE algorithm. Spiral readouts up to 25 ms are shown to permit whole-brain 2D imaging at 0.5 mm in-plane resolution in less than a minute. A range of options is explored, including proton-density and T₂* contrast, acceleration by parallel imaging, different readout orientations, and the extraction of phase images. Results are shown to exhibit competitive image quality along with high geometric consistency.

Improved MRI thermometry with multiple-echo spirals

PURPOSE

Low-bandwidth PRF shift thermometry is used to guide HIFU ablation treatments. Low sampling bandwidth is needed for high signal-to-noise ratio with short acquisition times, but can lead to off-resonance artifacts. In this work, improved multiple-echo thermometry is presented that allows for high bandwidth and reduced artifacts. It is also demonstrated with spiral sampling, to improve the trade-off between resolution, speed, and measurement precision.

METHODS

Four multiple-echo thermometry sequences were tested in vivo, one using two-dimensional Fourier transform (2DFT) sampling and three using spirals. The spiral sequences were individually optimized for resolution, for speed, and for precision. Multifrequency reconstruction was used to correct for off-resonance spiral artifacts. Additionally, two different multiecho temperature reconstructions were compared.

RESULTS

Weighted combination of per-echo phase differences gave significantly better precision than least squares off-resonance estimation. Multiple-echo 2DFT sequence obtained precision similar to single-echo 2DFT, while greatly increasing sampling bandwidth. The multiecho spiral acquisitions achieved 2× better resolution, 2.9× better uncertainty, or 3.4× faster acquisition time, without negatively impacting the other two design parameters as compared to single-echo 2DFT.

CONCLUSION

Multiecho spiral thermometry greatly improves the capabilities of temperature monitoring, and could improve transcranial treatment monitoring capabilities. Magn Reson Med 76:747-756, 2016. © 2015 Wiley Periodicals, Inc.

Fast higher-order MR image reconstruction using singular-vector separation

Medical resonance imaging (MRI) conventionally relies on spatially linear gradient fields for image encoding. However, in practice various sources of nonlinear fields can perturb the encoding process and give rise to artifacts unless they are suitably addressed at the reconstruction level. Accounting for field perturbations that are neither linear in space nor constant over time, i.e., dynamic higher-order fields, is particularly challenging. It was previously shown to be feasible with conjugate-gradient iteration. However, so far this approach has been relatively slow due to the need to carry out explicit matrix-vector multiplications in each cycle. In this work, it is proposed to accelerate higher-order reconstruction by expanding the encoding matrix such that fast Fourier transform can be employed for more efficient matrix-vector computation. The underlying principle is to represent the perturbing terms as sums of separable functions of space and time. Compact representations with this property are found by singular-vector analysis of the perturbing matrix. Guidelines for balancing the accuracy and speed of the resulting algorithm are derived by error propagation analysis. The proposed technique is demonstrated for the case of higher-order field perturbations due to eddy currents caused by diffusion weighting. In this example, image reconstruction was accelerated by two orders of magnitude.

Application of the fractional Fourier transform to image reconstruction in MRI

The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding.

Higher order reconstruction for MRI in the presence of spatiotemporal field perturbations

Despite continuous hardware advances, MRI is frequently subject to field perturbations that are of higher than first order in space and thus violate the traditional k-space picture of spatial encoding. Sources of higher order perturbations include eddy currents, concomitant fields, thermal drifts, and imperfections of higher order shim systems. In conventional MRI with Fourier reconstruction, they give rise to geometric distortions, blurring, artifacts, and error in quantitative data. This work describes an alternative approach in which the entire field evolution, including higher order effects, is accounted for by viewing image reconstruction as a generic inverse problem. The relevant field evolutions are measured with a third-order NMR field camera. Algebraic reconstruction is then formulated such as to jointly minimize artifacts and noise in the resulting image. It is solved by an iterative conjugate-gradient algorithm that uses explicit matrix-vector multiplication to accommodate arbitrary net encoding. The feasibility and benefits of this approach are demonstrated by examples of diffusion imaging. In a phantom study, it is shown that higher order reconstruction largely overcomes variable image distortions that diffusion gradients induce in EPI data. In vivo experiments then demonstrate that the resulting geometric consistency permits straightforward tensor analysis without coregistration.

k-space water-fat decomposition with T2* estimation and multifrequency fat spectrum modeling for ultrashort echo time imaging

PURPOSE

To demonstrate the feasibility of combining a chemical shift-based water-fat separation method (IDEAL) with a 2D ultrashort echo time (UTE) sequence for imaging and quantification of the short T(2) tissues with robust fat suppression.

MATERIALS AND METHODS

A 2D multislice UTE data acquisition scheme was combined with IDEAL processing, including T(2)* estimation, chemical shift artifacts correction, and multifrequency modeling of the fat spectrum to image short T(2) tissues such as the Achilles tendon and meniscus both in vitro and in vivo. The integration of an advanced field map estimation technique into this combined method, such as region growing (RG), is also investigated.

RESULTS

The combination of IDEAL with UTE imaging is feasible and excellent water-fat separation can be achieved for the Achilles tendon and meniscus with simultaneous T(2)* estimation and chemical shift artifact correction. Multifrequency modeling of the fat spectrum yields more complete water-fat separation with more accurate correction for chemical shift artifacts. The RG scheme helps to avoid water-fat swapping.

CONCLUSION

The combination of UTE data acquisition with IDEAL has potential applications in imaging and quantifying short T(2) tissues, eliminating the necessity for fat suppression pulses that may directly suppress the short T(2) signals.

Spiral demystified

Spiral acquisition schemes offer unique advantages such as flow compensation, efficient k-space sampling and robustness against motion that make this option a viable choice among other non-Cartesian sampling schemes. For this reason, the main applications of spiral imaging lie in dynamic magnetic resonance imaging such as cardiac imaging and functional brain imaging. However, these advantages are counterbalanced by practical difficulties that render spiral imaging quite challenging. Firstly, the design of gradient waveforms and its hardware requires specific attention. Secondly, the reconstruction of such data is no longer straightforward because k-space samples are no longer aligned on a Cartesian grid. Thirdly, to take advantage of parallel imaging techniques, the common generalized autocalibrating partially parallel acquisitions (GRAPPA) or sensitivity encoding (SENSE) algorithms need to be extended. Finally, and most notably, spiral images are prone to particular artifacts such as blurring due to gradient deviations and off-resonance effects caused by B(0) inhomogeneity and concomitant gradient fields. In this article, various difficulties that spiral imaging brings along, and the solutions, which have been developed and proposed in literature, will be reviewed in detail.

Iterative off-resonance and signal decay estimation and correction for multi-echo MRI

Signal dephasing due to field inhomogeneity and signal decay due to transverse relaxation lead to perturbations of the Fourier encoding commonly applied in magnetic resonance imaging. Hence, images acquired with long readouts suffer from artifacts such as blurring, distortion, and intensity variation. These artifacts can be removed in reconstruction, usually based on separately collected information in form of field and relaxation maps. In this work, a recently proposed gridding-based algorithm for off-resonance correction is extended to also address signal decay. It is integrated into a new fixed-point iteration, which permits the joint estimation of an image and field and relaxation maps from multi-echo acquisitions. This approach is then applied in simulations and in vivo experiments and demonstrated to improve both images and maps. The rapid convergence of the fixed-point iteration in combination with the efficient gridding-based correction promises to render the running time of such a joint estimation acceptable.

Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients

Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method.

Effect on BOLD sensitivity due to susceptibility-induced echo time shift in spiral-in based functional MRI

Susceptibility artifacts induced by the magnetic field inhomogeneity exist near the air/tissue interfaces at the ventral brain in functional magnetic resonance imaging (fMRI). These susceptibility artifacts will cause geometric distortions and signal loss in reconstructed images. Additionally, the in-plane susceptibility gradients will cause a shift in effective echo time, and therefore influence the blood-oxygen-level dependent (BOLD) sensitivity since it is proportional to effective echo time. In this work, we examine the effective echo time shift and the change of the BOLD sensitivity based on susceptibility gradients. The analysis results show that there are regions, such as the orbitofrontal cortex, that suffer from significant loss of BOLD sensitivity using spiral-in trajectory in BOLD fMRI.

Fast joint reconstruction of dynamic R2* and field maps in functional MRI

Blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) is conventionally done by reconstructing T(2)(*)-weighted images. However, since the images are unitless they are nonquantifiable in terms of important physiological parameters. An alternative approach is to reconstruct R(2)(*) maps which are quantifiable and have comparable BOLD contrast as T(2)(*)-weighted images. However, conventional R(2)(*) mapping involves long readouts and ignores relaxation during readout. Another problem with fMRI imaging is temporal drift/fluctuations in off-resonance. Conventionally, a field map is collected at the start of the fMRI study to correct for off-resonance, ignoring any temporal changes. Here, we propose a new fast regularized iterative algorithm that jointly reconstructs R(2)(*) and field maps for all time frames in fMRI data. To accelerate the algorithm we linearize the MR signal model, enabling the use of fast regularized iterative reconstruction methods. The regularizer was designed to account for the different resolution properties of both R(2)(*) and field maps and provide uniform spatial resolution. For fMRI data with the same temporal frame rate as data collected for T(2)(*)-weighted imaging the resulting R(2)(*) maps performed comparably to T(2)(*)-weighted images in activation detection while also correcting for spatially global and local temporal changes in off-resonance.

Semiautomatic off-resonance correction in spiral imaging

Spiral scanning is a promising MRI method, but one limitation is that off-resonance effects can cause image blurring. Most current off-resonance correction methods for spiral imaging require an accurate field map, which is difficult to obtain in many applications. Automatic methods can perform off-resonance correction without acquiring a field map. However, these methods are computationally inefficient and relatively prone to estimation error. This study describes a new semiautomatic off-resonance correction method that combines an automatic method with a low resolution field map acquisition for off-resonance correction in spiral scanning. Experiments demonstrate that this method is more robust than conventional automatic off-resonance correction and can provide more accurate off-resonance correction than conventional field map based methods. The proposed method is also computationally efficient and has been implemented for online reconstruction.

A least squares quantization table method for direct reconstruction of MR images with non-Cartesian trajectory

The direct Fourier transform method is a straightforward solution with high accuracy for reconstructing magnetic resonance (MR) images from nonuniformly sampled k-space data, given that the optimal density compensation function is selected and the underlying magnetic field is sufficiently uniform. The computation however is very time-consuming, making it impractical especially for large-size images. In this paper, the least squares quantization table (LSQT) method is proposed to accelerate the direct Fourier transform computation, similar to the recently proposed methods such as using look-up table (LUT) or equal-phase-line (EPL). With LSQT, all the image pixels are first classified into several groups where the Lloyd-Max quantization scheme is used to ensure the minimal classification error. The representative value of each group is stored in a small-size LSQT in advance to reduce the computational load. The pixels in the same group receive the same contribution, which is calculated only once for each group instead of for each pixel, resulting in the reduction of computation because the number of groups is far smaller than the number of pixels. Finally, each image pixel is mapped into the nearest group and its representative value is used to reconstruct the image. The experimental results show that the LSQT method requires far smaller memory size than the LUT method and fewer multiplication operations than the LUT and EPL methods. Moreover, the LSQT method can perform large-size reconstructions that achieve comparable or higher accuracy as compared to the EPL and gridding methods when the appropriate parameters are given. The inherent parallel structure also makes the LSQT method easily adaptable to a multiprocessor system.

Conjugate phase MRI reconstruction with spatially variant sample density correction

A new image reconstruction method to correct for the effects of magnetic field inhomogeneity in non-Cartesian sampled magnetic resonance imaging (MRI) is proposed. The conjugate phase reconstruction method, which corrects for phase accumulation due to applied gradients and magnetic field inhomogeneity, has been commonly used for this case. This can lead to incomplete correction, in part, due to the presence of gradients in the field inhomogeneity function. Based on local distortions to the k-space trajectory from these gradients, a spatially variant sample density compensation function is introduced as part of the conjugate phase reconstruction. This method was applied to both simulated and experimental spiral imaging data and shown to produce more accurate image reconstructions. Two approaches for fast implementation that allow the use of fast Fourier transforms are also described. The proposed method is shown to produce fast and accurate image reconstructions for spiral sampled MRI.

Reconstruction after rotational motion

Patient rotational motion during a scan causes the k-space sampling to be both irregular and undersampled. Conventional regridding requires an estimate of the sampling density at each measured point and is not strictly consistent with sampling theory. Here, a 2D problem is converted to a series of 1D regriddings by exact interpolation along the measured readouts. Each 1D regridding, expressed in matrix form, requires a matrix inversion to gain an exact solution. Undersampled regions make the matrix ill-conditioned but summing the matrix columns (without inversion) indicates the undersampled regions. The missing data could be reacquired, but in this study it is estimated using a Delaunay triangle-based linear interpolation on the original 2D data. The matrix conditioning is improved, leading to images with reduced artifacts compared to other regridding schemes. Furthermore, there is no requirement to estimate a density compensation function at each of the measured points.

MRI fast tree log scanning with helical undersampled projection acquisitions

Magnetic Resonance Imaging opens an alternative way to analyze wood structures using a non-destructive technology. It provides high resolution, compound-based contrast manipulation and increased data acquisition flexibility. The technique is particularly useful for tree logs, since they present several characteristics that can be used to reduce the long scan time. This study proposes a method that takes advantage of the log cylindrical symmetry, acquiring transverse 1-D projections with a helical and undersampled pattern. Linear interpolation is used to estimate the skipped data and slice images are reconstructed by filtered backprojection. The sequence is improved using selective multi-pass scanning, without major variations of the scan time. Computer simulations and experimental results show that the proposed technique can increase the scan speed by a factor of 6, while maintaining the ability to identify typical tree log characteristics.

Direct reconstruction of MR images from data acquired on a non-Cartesian grid using an equal-phase-line algorithm

The equal-phase line (EPL) algorithm is proposed as a means of allowing rapid Fourier transform (FT) reconstruction of MR image data acquired on a non-Cartesian grid. The pixels on the image are grouped according to their positions. The pixels in a group have the same phase in the complex exponential function -exp[j2pi(xu + yv)] and receive the same contribution from a data point. Each group is related to an EPL in the image space. The contribution of a data point can then be distributed to the pixels along the EPLs. The described EPL algorithm enables a decrease of the reconstruction time to about 40% of the direct FT (DrFT) for the non-Cartesian data. A numerical phantom and two sets of in vivo spiral data were used to investigate an optimal number of the EPLs and to measure the reconstruction time. The EPL algorithm runs nearly as fast as the look-up table (LUT) method (Dale et al. IEEE Trans Med Imaging 2001;20:207-217), but it does not require a large memory to store the coefficients in advance, as is required in the LUT method. Thus, the EPL algorithm can be used to reconstruct images up to 512 x 512 pixels in size in a PC of limited memory, and may be more conveniently applied to a multiprocessor system.

Off-resonance correction using an estimated linear time map

Images acquired in the presence of magnetic field deviations and reconstructed without taking into account the off-resonance, are distorted and corrupted with artifacts. Several post-processing algorithms have been developed for correcting the distortion when it is not possible to fix the field inhomogeneities. These off-resonance correction methods are, in general, slow and computing intensive. To make them faster they are usually adapted to a particular situation or approximated. One of these approximations is to assume that the field map is linear. Although this assumption makes the algorithm fast and robust it is not well suited for arbitrary field maps. On the other hand, there are k-space trajectories with an almost linear time map (time at which each k-space value is acquired), such as 2DFT and EPI. This paper presents an algorithm for off-resonance correction based on a linear time map approximation. This approximation allows a fast algorithm that takes advantage of the almost linearity of the time map and uses the whole field map to correct the images. The proposed correction algorithm reduces the off-resonance induced artifacts while being fast. The linear approximation of the time map needs to be done only once for each trajectory because it does not depend on the acquired image or field map data. The method can also be extended to a multi-plane approximation for sequences with more complex time maps.

Direct reconstruction of non-Cartesian k-space data using a nonuniform fast Fourier transform

An algorithm of Dutt and Rokhlin (SIAM J Sci Comput 1993;14:1368-1383) for the computation of a fast Fourier transform (FFT) of nonuniformly-spaced data samples has been extended to two dimensions for application to MRI image reconstruction. The 2D nonuniform or generalized FFT (GFFT) was applied to the reconstruction of simulated MRI data collected on radially oriented sinusoidal excursions in k-space (ROSE) and spiral k-space trajectories. The GFFT was compared to conventional Kaiser-Bessel kernel convolution regridding reconstruction in terms of image reconstruction quality and speed of computation. Images reconstructed with the GFFT were similar in quality to the Kaiser-Bessel kernel reconstructions for 256(2) pixel image reconstructions, and were more accurate for smaller 64(2) pixel image reconstructions. Close inspection of the GFFT reveals it to be equivalent to a convolution regridding method with a Gaussian kernel. The Gaussian kernel had been dismissed in earlier literature as nonoptimal compared to the Kaiser-Bessel kernel, but a theorem for the GFFT, bounding the approximation error, and the results of the numerical experiments presented here show that this dismissal was based on a nonoptimal selection of Gaussian function.

Reducing off-resonance distortion by echo-time interpolation

Off-resonant spins, produced by chemical shift, tissue-susceptibility differences, or main-field inhomogeneity, can cause blurring or shifts, severely compromising the diagnostic value of magnetic resonance images. To mitigate these off-resonance effects, the authors propose a technique whereby two images are acquired at different echo times (TEs) and interpolated to produce a single image with dramatically-reduced blurring. The phase difference of these two images is not used to produce a field map; instead, the weighted complex-valued average of the two images is used to produce a single image. Previously-described methods reconstruct a set of preliminary images, each at a different off-resonant frequency, and then assemble these into one final image, choosing the best off-resonant frequency for each voxel. Compared to these methods, the proposed technique requires the same or less processing time and is much less sensitive to errors in the field map. This technique was applied to centric-ordered EPI but it can be applied to any imaging trajectory, including one-shot EPI, spiral imaging, projection-reconstruction imaging, and 2D GRASE. Magn Reson Med 45:269-276, 2001.

Sampling and reconstruction effects due to motion in diffusion-weighted interleaved echo planar imaging

Subject motion during diffusion-weighted interleaved echo-planar imaging causes k-space offsets which lead to irregular sampling in the phase-encode direction. For each image, the k-space shifts are monitored using 2D navigator echoes, and are shown to lead to a frequent violation of the Nyquist condition when an ungated sequence is used on seven subjects. Combining data from four repeat acquisitions allows the Nyquist condition to be satisfied in all but 1% of images. Reconstruction of the irregularly-sampled data can be performed using a matrix inversion technique. The repeated acquisitions make the inversion more stable and additionally improve the signal-to-noise ratio. The resultant isotropic diffusion-weighted images and average apparent diffusion coefficient (ADC) maps show high resolution and enable clear localization of a stroke lesion. Residual ADC artifacts with a slow spatial variation are observed and assumed to originate from non-rigid pulsatile brain motion. Magn Reson Med 44:101-109, 2000.

Critical sampling in ROSE scanning

The acquisition of unaliased ROSE (Radially Oriented Sinusoidal Excursions in k-space) data requires the appropriate selection of a gradient frequency, number of interleaves, and number of data samples per acquisition. When the data samples are uniformly distributed in time, they fall on irregularly spaced circles in k-space. Aliasing due to radial undersampling will be eliminated when the number of sample circles equals the number of pixels in one dimension of the desired reconstructed image. Azimuthal aliasing will be completely eliminated when the total number of ROSE petals is four times the number of pixels in one dimension, but acceptable reconstructions may be had with fewer petals. Magn Reson Med 44:129-136, 2000.

A generalized k-sampling scheme for 3D fast spin echo

The phase-encoding scheme can significantly affect the quality of fast spin-echo (FSE) images because the echo amplitude is modulated as a function of the echo position in k-space. The effects of the modulation in two-dimensional FSE imaging include ghosting and blurring artifacts and resolution loss in the phase-encoding (PE) direction. In 3D FSE imaging, the use of two PE directions presents the opportunity for improved PE schemes. A new scheme for assignment of echoes to views in 3D FSE, termed generalized, has been developed. This scheme distributes T(2) effects along both PE directions, allowing considerable flexibility in the selection of blurring artifact appearance. In a set of simulations, phantom experiments, and in vivo experiments, the performance of the generalized PE scheme for 3D FSE imaging was compared with the performance of existing PE schemes. The results demonstrate that the generalized PE scheme can be used to reduce blurring artifacts greatly relative to other PE techniques that are presently in use. This approach to PE can be used to manipulate the blurring artifact appearance and to optimize acquisition time.

Improvements in spiral MR imaging

The basic principles of spiral MR image acquisition and reconstruction are summarised with the aim to explain how high quality spiral images can be obtained. The sensitivity of spiral imaging to off-resonance effects, gradient system imperfections and concomitant fields are outlined and appropriate measures for corrections are discussed in detail. Phantom experiments demonstrate the validity of the correction approaches. Furthermore, in-vivo results are shown to demonstrate the applicability of the corrections under in-vivo conditions. The spiral image quality thus obtained was found to be comparable to that obtainable with robust spin warp sequences.

Off-resonance correction of MR images

In magnetic resonance imaging (MRI), the spatial inhomogeneity of the static magnetic field can cause degraded images if the reconstruction is based on inverse Fourier transformation. This paper presents and discusses a range of fast reconstruction algorithms that attempt to avoid such degradation by taking the field inhomogeneity into account. Some of these algorithms are new, others are modified versions of known algorithms. Speed and accuracy of all these algorithms are demonstrated using spiral MRI.

Iterative reconstruction of single-shot spiral MRI with off resonance

A variety of applications and research directions in magnetic resonance imaging which require fast scan times have recently become popular. In order to satisfy many of the requirements of these applications, snapshot imaging methods, which acquire an entire image in one excitation, are often used. These snapshot techniques are relatively insensitive to motion and can allow rapidly occurring processes to be imaged. However, snapshot imaging techniques acquire data over a relatively long period, during which off-resonance phase can accumulate, leading to image degradation. This degradation often limits the usefulness of the images. Presented here is a method to iteratively reconstruct an image acquired by a spiral snapshot technique and to remove image degradation due to off resonance. This iterative method does not assume that the inhomogeneity is slowly varying within the image, allowing better results than with deblurring techniques which do not take abrupt changes into account. Although presented here with a spiral imaging technique, the iterative algorithm is general enough to be applied to a variety of snapshot imaging techniques.

On spatially selective RF excitation and its analogy with spiral MR image acquisition

The basic principles of the design of spatially selective RF pulses are described, and their analogy with MR image acquisition and reconstruction is shown. The paper focuses on RF-pulse design and imaging schemes in which spiral k-space trajectories are used. The sensitivity of RF excitation to gradient-system imperfections and to spatially varying off-resonance are analyzed, and suitable measures of correction are discussed. The spatial resolution obtainable with selective RF pulses and the consequences of the linearity of the pulse-design problem are examined. Phantom experiments showing the performance of multidimensional spatially selective RF pulses further illustrate the analogy with MR image acquisition.

An optimal and efficient new gridding algorithm using singular value decomposition

The problem of handling data that falls on a nonequally spaced grid occurs in numerous fields of science, ranging from radio-astronomy to medical imaging. In MRI, this condition arises when sampling under time-varying gradients in sequences such as echo-planar imaging (EPI), spiral scans, or radial scans. The technique currently being used to interpolate the nonuniform samples onto a Cartesian grid is called the gridding algorithm. In this paper, a new method for uniform resampling is presented that is both optimal and efficient. It is first shown that the resampling problem can be formulated as a problem of solving a set of linear equations Ax = b, where x and b are vectors of the uniform and nonuniform samples, respectively, and A is a matrix of the sinc interpolation coefficients. In a procedure called Uniform Re-Sampling (URS), this set of equations is given an optimal solution using the pseudoinverse matrix which is computed using singular value decomposition (SVD). In large problems, this solution is neither practical nor computationally efficient. Another method is presented, called the Block Uniform Re-Sampling (BURS) algorithm, which decomposes the problem into solving a small set of linear equations for each uniform grid point. These equations are a subset of the original equations Ax = b and are once again solved using SVD. The final result is both optimal and computationally efficient. The results of the new method are compared with those obtained using the conventional gridding algorithm via simulations.

Algebraic reconstruction for magnetic resonance imaging under B0 inhomogeneity

In magnetic resonance imaging, spatial localization is usually achieved using Fourier encoding which is realized by applying a magnetic field gradient along the dimension of interest to create a linear correspondence between the resonance frequency and spatial location following the Larmor equation. In the presence of B0 inhomogeneities along this dimension, the linear mapping does not hold and spatial distortions arise in the acquired images. In this paper, the problem of image reconstruction under an inhomogeneous field is formulated as an inverse problem of a linear Fredholm equation of the first kind. The operators in these problems are estimated using field mapping and the k-space trajectory of the imaging sequence. Since such inverse problems are known to be ill-posed in general, robust solvers, singular value decomposition and conjugate gradient method, are employed to obtain corrected images that are optimal in the Frobenius norm sense. Based on this formulation, the choice of the imaging sequence for well-conditioned matrix operators is discussed, and it is shown that nonlinear k-space trajectories provide better results. The reconstruction technique is applied to sequences where the distortion is more severe along one of the image dimensions and the two-dimensional reconstruction problem becomes equivalent to a set of independent one-dimensional problems. Experimental results demonstrate the performance and stability of the algebraic reconstruction methods.

Simulated phase evolution rewinding (SPHERE): a technique for reducing B0 inhomogeneity effects in MR images

A novel method for reducing field inhomogeneity effects in magnetic resonance images is described in this paper. Observing that image degradation arises from B0 inhomogeneity-induced phase accrual during data acquisition, the present method numerically rewinds the accumulated phase in the k-space data based on an initial estimate of the image and a corresponding field map. The rewinding process generates a corrected k-space data set that is subsequently Fourier transformed to produce the final image. In this paper, a theoretical analysis of the method and applications of the technique to magnetic resonance imaging data are presented. The theoretical analysis of the method indicates that it is a general approach applicable to a variety of sequences. Results obtained by applying the method to experimental data acquired with single-shot echo-planar imaging, segmented echo-planar imaging with centric reordering, and spiral sequences demonstrate that it is robust in reducing image degradation induced by B0 inhomogeneity.

Dynamic shimming for multi-slice magnetic resonance imaging

Dynamic shimming has been implemented in three pulse sequences on a commercial GE Signa 1.5-T imaging system. Multi-slice field maps are acquired before the imaging sequence, and linear shim terms and center frequencies are calculated for each slice. During the imaging scan, the linear shim terms and center frequency are set before each pulse sequence repetition according to the current slice. Acquisition of multi-slice field maps and calculation of shim terms and center frequency for each slice are accomplished in a matter of seconds. Pulse sequences require only minimal modification to add dynamic shimming capability. Results are shown for a fat saturation spin-echo sequence, a single-shot echo-planar gradient-recalled echo sequence, and a spiral acquisition gradient-recalled echo sequence. In all cases, dynamic shimming with shim currents and center frequency optimized for each slice is shown to give better results than constant shim currents and a single center frequency optimized for the entire volume of interest.

Improved automatic off-resonance correction without a field map in spiral imaging

Non-2DFT k-space readout strategies are useful in fast imaging but prone to blurring when reconstructed off resonance. Field inhomogeneities or susceptibility variations, coupled with a long readout time, are the major sources of this artifact. Correction methods based on a priori off-resonance information such as an acquired field map have been proposed in the literature. An alternative approach estimates the spatially varying off-resonance frequency from the data itself before applying a correction. In this latter approach there is a trade-off between the extent of correction and the chance of increased artifact due to estimation error. This paper introduces an improved algorithm for field map estimation which is both faster and more robust than the existing method. It uses a multi-stage estimation of the field map, starting from a coarse estimate both in frequency and space and proceeds towards higher resolution. The new algorithm is applied to phantom and in vivo images acquired with radial and spiral sequences to give sharper images.

Multifrequency interpolation for fast off-resonance correction

Field inhomogeneities or susceptibility variations produce blurring in images acquired using non-2DFT k-space readout trajectories. This problem is more pronounced for sequences with long readout times such as spiral imaging. Theoretical and practical correction methods based on an acquired field map have been reported in the past. This paper introduces a new correction method based on the existing concept of frequency segmented correction but which is faster and theoretically more accurate. It consists of reconstructing the data at several frequencies to form a set of base images that are then added together with spatially varying linear coefficients derived from the field map. The new algorithm is applied to phantom and in vivo images acquired with projection reconstruction and spiral sequences, yielding sharply focused images.

RARE spiral T2-weighted imaging

Spiral imaging has a number of advantages for fast imaging, including an efficient use of gradient hardware. However, inhomogeneity -induced blurring is proportional to the data acquisition duration. In this paper, we combine spiral data acquisition with a RARE echo train. This allows a long data acquisition interval per excitation, while limiting the effects of inhomogeneity. Long spiral k-space trajectories are partitioned into smaller, annular ring trajectories. Each of these annular rings is acquired during echoes of a RARE echo train. The RARE refocusing RF pulses periodically refocus off-resonant spins while building a long data acquisition. We describe both T2-weighted single excitation and interleaved RARE spiral sequences. A typical sequence acquires a complete data set in three excitations (32 cm FOV, 192 x 192 matrix). At a TR = 2000 ms, we can average two acquisitions in an easy breath-hold interval. A multifrequency reconstruction algorithm minimizes the effects of any off-resonant spins. Though this algorithm needs a field map, we demonstrate how signal averaging can provide the necessary phase data while increasing SNR. The field map creation causes no scan time penalty and essentially no loss in SNR efficiency. Multiple slice, 14-s breath-hold scans acquired on a conventional gradient system demonstrate the performance.